Question

Given parallelogram ABCD. If m∠ACD = (7x – 12)° and m∠BDC = (10x + 5)°, find x. Write your response in the form x=_____.

Answer 1

Given:

In the parallelogram ABCD, m∠ACD = (7x – 12)° and m∠BDC = (10x + 5)°.

To find:

The value of x.

Solution:

The diagonals of a parallelogram are perpendicular bisectors.

Let O be the intersection point of the diagonals.

In triangle OCD,

$m\angle OCD+m\angle ODC+m\angle COD=180^\circ$       [Angle sum property]

$(7x-12)+(10x+5)+90=180$

$17x+83=180$

$17x=180-83$

$17x=97$

$x=\dfrac{97}{17}$

Therefore, the value of x is equal to $\dfrac{97}{17}$.